I would say yes you have a Red Underwing here, the outer markings can be a bit similar between this family of moths, so its often a good idea to look at the underwing as those are different on each, but the Red Underwing has a less denated (wavy) sub terminal line. That link explains the differences.

That's fantastic, thanks to you both! I was hoping I'd gotten it right. I didn't want to disturb him or potentially damage him otherwise I'd have tried to get him to spread his impressive wings..............He looked very peaceful!